id: 02364093
dt: a
an: 2005e.02389
au: Fung, David; Ligh, Steve
ti: Trigonometric representation of $\lbrack$x$\rbrack$.
so: Bogacki, Przemyslaw (ed.), Proceedings of the 7th annual international
conference on technology in collegiate mathematics, ICTCM 7, Orlando,
FL, USA, November 17â€’20, 1994. Norfolk, VA: Old Dominion University,
Dept. of Mathematics and Statistics (ISBN 0-201-87020-7). Electronic
paper (1994).
py: 1994
pu: Norfolk, VA: Old Dominion University, Dept. of Mathematics and Statistics
la: EN
cc: I25 R25
ut: greatest integer function; applications of mathematics to mathematics;
trigonometric functions; proofs; computer algebra
ci:
li:
ab: In the software DERIVE (version 2.07), the greatest integer function,
$\lbrack$x$\rbrack$, when simplified, is given as $\lbrack$x$\rbrack$ =
arctan(cot(pi*x))/pi + x - 1/2. The above equality can be proved by
means of properties of trigonometric functions. Using other inverse
trigonometric functions, we obtain several forms for
$\lbrack$x$\rbrack$ as well as other step-like functions. (authorsâ€™
abstract) (The paper is available under
http://archives.math.utk.edu/ICTCM/abs/7-FB17.html)
rv: